It can be difficult to directly sense very high voltages, such as voltages of many kilovolts. As shown in FIG. 3, a high voltage sensing circuit 30 can comprise resistors in series 11 to indirectly sense very high voltages. A first resistor r1, having a relatively small resistance R1, can be electrically connected in series 11 with a second resistor r2, having a relatively large resistance R2. The difference in resistances of the resistors can be very large. For example, the larger resistance R2 divided by the smaller resistance R1 can be about 1000.
The series 11 can be connected across a device 15 having a very high voltage differential, such that one end of the series 11 is connected to a lower voltage section of the device 15 and another end of the series 11 is connected to a higher voltage section. Either end 13 or 14 can be the lower voltage section and the opposing end can be the higher voltage section. The high and low voltage sections 13 and 14 can be separated by insulative material 17. The insulative material 17 can be air. The insulative material 17 can be an insulative tube, such as an x-ray tube.
Because of the small resistance R1 of the first resistor r1 in the series 11 compared to a sum of the resistances of the two resistors (R1+R2), the voltage V1 across the first resistor r1 can be relatively small and can be measured more easily than the relatively large voltage VT across the entire device 15. The voltage V1 across the first resistor r1 can be used to calculate the voltage VT across the device 15 by the equation:
      V    T    =      V    ⁢                  ⁢    1    *                                        R            ⁢                                                  ⁢            1                    +                      R            ⁢                                                  ⁢            2                                    R          ⁢                                          ⁢          1                    .      
The equation:
      V    T    =      V    ⁢                  ⁢    1    *                            R          ⁢                                          ⁢          1                +                  R          ⁢                                          ⁢          2                            R        ⁢                                  ⁢        1            can provide an accurate indication of the voltage VT across the device 15 if the resistors r1 & r2 are maintained at the same temperature. In reality, each resistor can have a different temperature from the other resistor, and a single resistor can even have temperature differentials across the single resistor. Temperature changes can cause resistances of the resistors to change, and uneven temperature changes across the resistors, or of one resistor compared to another resistor, can result in an inaccurate indication of the voltage VT across the device.
This temperature dependence of the resistors can be shown by the equation: R=Rref[1+α(T−Tref)] in which R is the resistance at temperature T, Rref is the resistance at a reference temperature Tref, and α is a temperature coefficient of resistance for the resistive material.
The resistors can be surface mount, and for very large resistances, which are needed for sensing very large voltages, such as around tens of kilovolts, the surface mount resistor can be several centimeters long. If the sensing circuit 30 is used for sensing x-ray tube voltage, one end of the series 11 can be disposed near the x-ray tube cathode and can be heated by the cathode. The other end, farther from the cathode, may be heated less, thus resulting in substantial temperature differential across the series 11 of resistors. This temperature differential can result in an inaccurate indication of the actual tube voltage. The user of the x-ray tube can thus have a different x-ray output spectrum than desired or than expected based on the indication of the tube voltage.
It would be beneficial to be able to correct for inaccuracies, caused by temperature differentials of the resistors, in order to obtain a more accurate device voltage.